I had to go to a family gathering over the weekend. I spoke with one who is currently working on his PhD in Chemical Engineering. He is working with polymers in an interesting way.
He and I discussed the skills he needs in his line of work. It came out he doesn't bother keeping track of certain chemical interactions because he looks it up anytime.
We also discussed when he needs to do any type of data analysis, he has programs to complete the analysis. He does not worry about remembering various formulas.
He stated, it is more important for him to know how to use these programs and interpret the results than it is to remember how to do it by hand. I found that interesting because the school system is still way behind this belief.
It does emphasis the idea that math provides answers and its important for students to interpret the results they get from their calculations. I don't do this enough. I teach students how to solve equations but I do not take the extra time to ask them to interpret their answers in terms of the problem.
I have them solve one and two step equations but I do not take the time to discuss what the answer might represent. When I studied math in high school, it was only important to solve equations, not understand anything about the meaning of the results. That was not important.
According to current thinking, it is important for students to be able to create mathematical observations about their solutions. They need to connect the mathematics with the situation. One facet of a mathematically proficient student is their ability to interpret results in context of the situation and reflecting if their solution makes sense.
They are able to take this reflection and make changes to create a model which is closer to what it should be. This is a real life process. The young man, talked about using the results of the data he's collected to determine what the next step should be. He adjusts factors, tests, and recalculates.
Having students work on performance tasks which require them to examine their works to find tune their assumptions is important and used more in life than having a problem done once and accepting the answer is done so you have nothing more left.
Yes, it sounds like a science experiment but if you are creating a mathematical model of a situation, it often takes several tries to get the right equation. It seldom happens immediately with the first try. Its important to create a situation to help students create models which take several tries to get right.
Let me know what you think. I'd love to hear.